Functions and Quotient

Question

Let f(x) be the function 1 / x+5. Then the quotient f(5+ℎ)-f(5) / h can be simplified to -1 / aℎ+b for:

a=

and

b= 

(I've been able to get a, which is 10 but for some reason I keep getting b as 0 and that's not correct.)

Answer 1

f(x) = 1/(x+5)

f(5+h) - f(5) = 1 / (10+h) - 1/10 = [10 - (10+h)] / [10(10+h)] = -h / [10(10+h)]

So, [f(5+h) - f(5)] / h = (-h/ [10(10+h)]) / h = (-h / [10(10+h)]) (1/h) = -1 / [10(10+h)] = -1 / (10h + 100)